1

SOC 3811

Basic Social Statistics

2

Announcements

Assignment 2 Revisions (interpretation of measures of central tendency and dispersion)—due next lab.

No midterm exam revision policy.

3

Class overview

Concept review

- descriptive v.s. influential statistics

- null and alternative hypotheses

- test statistics (sampling distributions)

- type 1 and type 2 errors

M & M activities

4

Inferential Statistics

Descriptive statistics:

to describe or summarize the data of a sample

Inferential statistics:

to make generalizations about a population using a sample

eg: GSS —> the American Population

(estimators parameters )

5

Necessary conditions for inference

With a large enough N. It is representative. It’s a random sample. (We take it at lots of different times and places.)

Usually if the sample is truly random, it will also be representative.

6

How to make inferences?

Need to do hypothesis testing!

Steps:1. create your hypotheses2. random sampling3. make statistical tests4. draw the conclusion (reject or accept your

hypothesis. )

7

Test the null hypothesis

Create hypotheses: the null hypothesis and alternative

hypothesis should be mutually exclusive. Get the “estimates” from random samples. Test if the estimate is a close estimate?

(Hint: if the null hypothesis is true, what are the expected behaviors of some test statistics? Compare if these test statistics behave close enough. )

8

Sampling distributions

Central Limit Theorem

9

Test statistics

z, t, χsquare, F.

specify α: we can set an acceptable confidence interval (/ probability of type 1 error, usually it’s .05)

Compare the value of the statistic with the expected test statistic.

n

Xz

/0

10

Type of errors

The null hypothesis is actually true

The null hypothesis is

not true

Reject Type 1 error O

Accept O Type 2 error

11

Examples

12

M&M Activity

http://us.mms.com/us/about/products/

Don’t eat your candies before you count them!!

13

Hypothesis Test: Steps

State research hypothesis State null hypothesis Choose a probability of type 1 error. (This tells

you how sure you want to be, 90%, 95%, 99%, etc.)

Run an analysis in SPSS. (Determine mean and s.d. and significance level.)

Compare the results to the predetermined values in steps 2 & 3.

Decide whether you will accept or reject the null hypothesis.

14

Hypotheses?

H0: p = .24

Ha: p ≠ .24

15

Test statistic

n

Xz

/0

16

Conclusion?

for α=.05 (95% confidence level), Z=1.96 (Table D.2 in the textbook)

Our conclusion?